The battle over the future of the Market Basket grocery store chain continues, with the board of directors weighing an offer from fired CEO Arthur T. Demoulas to buy the company, while hundreds of workers loyal to him continue to demand that he be reinstated. In the meantime, the standoff between the warring sides of the Demoulas family is reportedly taking a toll on business, and even Gov. Deval Patrick has offered to mediate the dispute between Arthur T. and his cousin, Arthur S. who chairs the board. It leads us to ask: